 Hello and welcome to the session. In this session, we are going to discuss the following question and the question says that identify whether the following curves are simple, closed or both. Now let us start with the solution of the given question. Now let us discuss the first curve. We know that a simple curve does not intersect itself except if the starting and the finishing points are same and a closed curve is that curve whose starting and finishing points coincide. A closed curve can be drawn with same starting and finishing point. Now if we see this curve we see that it does not intersect anywhere so it is a simple curve but as it is starting and finishing points are different so it is not a closed curve So we write it is a simple curve but not closed. Let us see the second curve. See this curve does not intersect itself at any point so it is a simple curve. Also if we draw this curve we will start from one point and draw the curve and will stop at the same point so it is a closed curve. So we can write it is a simple closed curve. Now let us see the third curve. See the curve intersects itself at two points so it is not a simple curve but we can draw this curve with same starting and finishing point. That is we can draw this curve with same starting and finishing point like this. So it is a closed curve so we write it is a closed curve but not simple. This is the required solution. This completes our session. Hope you enjoyed this session.